MinT - Best Known (106, 106+49, s)-Nets in Base 3

Best Known (106, 106+49, s)-Nets in Base 3

(106, 106+49, 156)-Net over F₃ — Constructive and digital

Digital (106, 155, 156)-net over F₃, using

13 times m-reduction [i] based on digital (106, 168, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 84, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(106, 106+49, 302)-Net over F₃ — Digital

Digital (106, 155, 302)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+49, 5624)-Net in Base 3 — Upper bound on s

There is no (106, 155, 5625)-net in base 3, because

1 times m-reduction [i] would yield (106, 154, 5625)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30 083900 485843 456477 067315 408688 239151 722450 837376 847829 242067 559474 284001 > 3¹⁵⁴ [i]